Grade level: Grade 9 Content: Relations and Functions
Lesson: Identifying Relations and Functions
NextGeneration Sunshine StateStandards/Benchmarks: A. 2.3 Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions. SSS MA.D.1.4.1 and MA.D.1.4.2 HCTM Standard: Understanding patterns, relations and functions. HCTM Standards: problem solving: Build new mathematical knowledge through problem solving. Prior knowledge HCTM standard: Understanding numbers, ways of representing numbers, relationships among numbers and number systems.
Lesson Objective: Upon completion of the assignment, the students differentiate between the vocabulary words and know their meanings and function. Students will know how to plot points on a graph and know the domain and range of those points. The Students will identify relations and functions. Students will graph relations and Functions. TSW use behaviors that promote appropriate student interaction within physical surroundings. Use behaviors that enhance self-control, self-reliance, and self-esteem. They will identify the coordinates of the intersection of two lines. Students will understand and differentiate between the vocabulary terms. Students will understand the relationship between how graphs can be used to plot a function. Students will practice by using real world problems such as a can food drive and how the student’s numbers and the number of can’s that can be plotted on a graph.
Alternative outcomes/objectives: Have the students wrote some” if…then…” statements to summarize how they can determine whether a relation is a function. Have students write that describe the definition, the vertical-line test, the mapping diagrams and the repetition of the domain value. Students will utilize computer algebra program for reinforcement and practice. HCTM Standard: Understanding patterns, relations and functions. Prior knowledge HCTM standard: Understanding numbers, ways of representing numbers, relationships among numbers and number systems.
Prior Knowledge/Preskills:Students will be familiar with the terms and the number line. From this knowledge, they will be able to plot an ordered pair and know where to put it on the coordinating plain. They will identify the coordinates of the intersection of two lines. Students will understand and differentiate between the vocabulary terms. ESOL/ESS Strategy: Compare and contrast the answers with other students, work in small groups when needed.
Materials: Vocabulary words, Prentice Hall Mathematics Pre-Algebra book on page 400-404. Overhead projector or white board. Computers with web access Pencils, paper and a four function calculator ESE-Plastic disk for counting and adding the cans ESE-Handouts for visual aids. Rubric for assignment, alternative assessments and graphic organizer for vocabulary word definitions.
Motivation: Students will participate in a food drive for the hungry, this exercise will show students how to implement math into everyday activities, and real world problems. Students will learn to graph and plot that graph for actual cans collected. The motivation will be to help others in our community as well as the region.
Teacher-directed Instruction Model of Instruction: Direct and Cooperative learning Lesson Procedures-Lesson Introduction*:
Content Teacher
Special Education Teacher
-Opening Teacher will instruct the students to open their books to page 400 where TTW give the vocabulary words, TSW write them down and have the definitions for each. -Overview TTW will explain the graphing of the can goods on page 401 and ask students that brought cans to address the total in each class. Tell students to work in cooperative groups. All students will use an outline handout to take notes during the class discussion. Write the vocabulary words and their number counterparts on their handouts. -Review TSW recall the words as the teacher calls them out. Ask students to give definitions in their own words for clarification. Teaching support will include but are not limited to practice, reteaching, enrichment, assessment, reading and literacy, and Spanish activities. Define vocabulary words on the white board and out loud for students understanding. ESOL Strategy: Identify main ideas and vocabulary
-Opening TTW help students with their vocabulary words. TTW give students a work sheet with the definitions and vocabulary words and help them match them. TTW will read to students who need help with decoding the words. -Overview : TSW will open their books to page 400 and use the visual graphs for clarity. TTW will show them where it is and how to use the graph. TSW have round disk to help with counting of the cans to add them all together for the final numbers and to graph them on the graph. Check for understanding. TTW hand out 4 function calculators to students, and show them how to use them to add and subtract the different totals to find out who has the most cans collected. Students will be able to total the cans collected for the week and give each class a total number of cans. This will in turn be graphed in the plotted pairs. ESOL Strategy: analyze, complete, define, defend and debate
-Review : Immediate feedback, show students patterns in their mistakes so that they understand what they are doing wrong. Encourage students to review terms and how the words interchange with the math. Knowing the terms will help them understand the math problems, In addition, how to graph an ordered pair.
-Expectations TSW learn the terms and how they are used in algebra problems. TSW will be able to take an ordered pair and plot it on the graph. TSW understand the terms of the operations to know how to graph ordered pairs and will learn how to plot a graph. The students will work in cooperative groups and define terms, relations and functions of the graph.
-Rationale This lesson is taught so that students understand the graphs and the beginning of linear equations. Teaches students strategies and gives them practice with all the test item formats they will encounter on the FCAT. Error prevention: Students may forget to label their graphs. Suggest that the students begin a graph by labeling both axes. Remind them that time is often represented along the x-axis. -Guiding Questions
Guided Practice: Lead and Support*
Content Teacher
Special Education Teacher
TTW will tell students that they need their books on page 400 and to write down the terms and definitions. TTW guide them through the terms and show them where they are on the page. This can be done with the white board and the Elmo. TTW will explain about domain, range and how they work together on the coordinating plain, and show them how the Vertical-line test works to check their answers. TSW ask related questions and check for understanding. Students will be able to ask their cooperative partners and check for understanding. TTW explain the graph on page 400 about the can food drive. There are e6 homeroom classes that are participating in the can food drive, in those classes there are a different about of students in each class. The there are different amounts of cans that were brought in from each class. How does this relation, a set of ordered pairs. Discuss range, domain, and function. ESOL Strategy: Explain the process, predict, Think, share and compare.
Mentor role Review directions with students in small group or individually before using the handout. Review terms and definitions. Review reasoning and concepts with students Provide immediate feedback about performance. Check for understanding. Size: TSW follow along as other students or teacher. Give oral answers as questions are asked.
Input: TTW On over head projector discuss the questions with the class. Having students write down important facts, things that you wrote on the overhead can be given to the student to take home for reinforcement of concepts. ESOL Strategy: Give more details, simple details and answers
Output: TTW respond to questions at a lower level and the student will be able to answer fewer questions than the rest of the class. TTW be able to pick out the vocabulary words and read them out loud to the student. TSW be able to answer orally questions from the worksheet that was sent home as an assessment of progress
-Closure
Independent Practice/Cooperative Practice*
Content Teacher
Special Education Teacher
Graphing relations and functions, page 401-403. Students will work through problems with there cooperative partners. Provide web access to programs for FCAT review and math concepts practice. Chapter 8 on www.phschool.com for guided practice.
Substitute Curriculum: TSW have fewer questions to answer, will use vocabulary words as an alterative quiz, and have a reading buddy to help with the questions and the vocabulary words. TTW assess with oral questions and give the quiz while the other students are taking their quiz. TSW be able to have extra time if needed on quizzes and test.
Difficulty: TSW answer questions given on a work sheet.. Such as: Vocabulary words What o you think you need to do next, what is the next step?
Assessment*: Teachers learn about student learning through multiple ways: observations, asking questions, product completion, quizzes, verbal discussions, etc. to determine mastery of lesson objectives.
Content Teacher
Special Education Teacher
TTW observe students as they are working independently and in cooperative groups. TTW give feedback on answers she observes and help students and cooperative groups correct their answers. Immediate feedback is key to assessing students progress.
TTW have students who are ready to proceed to address the rest of the problems on pages 402- 404
Level of Support: TTW help student with answers, leading questions like what did you like about the problems? A peer Buddy (Reading Buddy) will help student with words that they do not know and will help student sound out words that are not mastered.
Time: Reread text and work sheet if necessary, so that student can listen for the answers. TSW be allowed to answer fewer questions so that they can finish the test in the same time frame as the rest of the class.
Degree of Participation: TSW answer the questions that are given. This will be fewer than the rest of the class so that the student can finish in the same time frame. If the student needs a break, the student will be able to get up and sharpen their pencil or get a drink.
Alternate Goals: TSW answer the same questions. They will be able to give simple answers. The student will have a reading buddy to help with the correct answers before the quiz. The quiz will be on vocabulary words and simple answer questions. There will be one higher level thinking question so that the student can get used to those kinds of questions for the standardized test.
*From Co-teaching rubric: The lesson plan reflects opportunities to work collaboratively with other professionals (e.g., co-teacher) in the continuous improvement of the educational experiences of students.
Extensions:
TSW have fewer questions to answer, will use vocabulary words as an alterative quiz, and have a reading buddy to help with the questions and the vocabulary words. TTW assess with oral questions and give the quiz while the other students are taking their quiz. TSW be able to have extra time if needed on quizzes and test.
Accommodations/Modifications:
The accommodations are in the plan size, input, output etc…
Access Points:
Independent: MA.912A.2 In.c. Identify the mathematical relationship (function) and the type of information represented in a function table or simple graph. Supported: MA.912.A.Su.c Identify number patters and relationships using physical and visual models representing real-world situations. Participatory: MA.912.A.2 Pa.b Compare sets to 10 of objects, pictures, or symbols using one-to-one correspondence and identify which has more or less.
Four labeled ESOL Strategies
ESOL Strategy: Give more details, simple details and answers. ESOL Strategy: analyze, complete, define, defend and debate. ESOL Strategy: Explain the process, predict, Think, share and compare. ESOL Strategy: Identify main ideas and vocabulary
References
Prentice Hall Mathematics Pre- Algebra Book. Students will access this website from the book to have extra practice in the class and at home. www.phschool.com
Lesson: Identifying Relations and Functions
NextGeneration Sunshine StateStandards/Benchmarks: A. 2.3 Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions.
SSS MA.D.1.4.1 and MA.D.1.4.2
HCTM Standard: Understanding patterns, relations and functions. HCTM Standards: problem solving: Build new mathematical knowledge through problem solving. Prior knowledge HCTM standard: Understanding numbers, ways of representing numbers, relationships among numbers and number systems.
Lesson Objective: Upon completion of the assignment, the students differentiate between the vocabulary words and know their meanings and function. Students will know how to plot points on a graph and know the domain and range of those points. The Students will identify relations and functions. Students will graph relations and Functions. TSW use behaviors that promote appropriate student interaction within physical surroundings. Use behaviors that enhance self-control, self-reliance, and self-esteem. They will identify the coordinates of the intersection of two lines. Students will understand and differentiate between the vocabulary terms. Students will understand the relationship between how graphs can be used to plot a function. Students will practice by using real world problems such as a can food drive and how the student’s numbers and the number of can’s that can be plotted on a graph.
Alternative outcomes/objectives: Have the students wrote some” if…then…” statements to summarize how they can determine whether a relation is a function. Have students write that describe the definition, the vertical-line test, the mapping diagrams and the repetition of the domain value. Students will utilize computer algebra program for reinforcement and practice. HCTM Standard: Understanding patterns, relations and functions. Prior knowledge HCTM standard: Understanding numbers, ways of representing numbers, relationships among numbers and number systems.
Prior Knowledge/Preskills: Students will be familiar with the terms and the number line. From this knowledge, they will be able to plot an ordered pair and know where to put it on the coordinating plain. They will identify the coordinates of the intersection of two lines. Students will understand and differentiate between the vocabulary terms. ESOL/ESS Strategy: Compare and contrast the answers with other students, work in small groups when needed.
Vocabulary Words: Relation, domain, range, function, coordinating plain, ordered pairs, axis.
Materials:
Vocabulary words, Prentice Hall Mathematics Pre-Algebra book on page 400-404.
Overhead projector or white board.
Computers with web access
Pencils, paper and a four function calculator
ESE-Plastic disk for counting and adding the cans
ESE-Handouts for visual aids.
Rubric for assignment, alternative assessments and graphic organizer for vocabulary word definitions.
Motivation: Students will participate in a food drive for the hungry, this exercise will show students how to implement math into everyday activities, and real world problems. Students will learn to graph and plot that graph for actual cans collected. The motivation will be to help others in our community as well as the region.
Teacher-directed Instruction
Model of Instruction: Direct and Cooperative learning
Lesson Procedures-Lesson Introduction*:
Teacher will instruct the students to open their books to page 400 where TTW give the vocabulary words, TSW write them down and have the definitions for each.
-Overview TTW will explain the graphing of the can goods on page 401 and ask students that brought cans to address the total in each class. Tell students to work in cooperative groups. All students will use an outline handout to take notes during the class discussion. Write the vocabulary words and their number counterparts on their handouts.
-Review TSW recall the words as the teacher calls them out. Ask students to give definitions in their own words for clarification. Teaching support will include but are not limited to practice, reteaching, enrichment, assessment, reading and literacy, and Spanish activities.
Define vocabulary words on the white board and out loud for students understanding.
ESOL Strategy: Identify main ideas and vocabulary
-Overview : TSW will open their books to page 400 and use the visual graphs for clarity. TTW will show them where it is and how to use the graph. TSW have round disk to help with counting of the cans to add them all together for the final numbers and to graph them on the graph. Check for understanding. TTW hand out 4 function calculators to students, and show them how to use them to add and subtract the different totals to find out who has the most cans collected. Students will be able to total the cans collected for the week and give each class a total number of cans. This will in turn be graphed in the plotted pairs.
ESOL Strategy: analyze, complete, define, defend and debate
-Review : Immediate feedback, show students patterns in their mistakes so that they understand what they are doing wrong.
Encourage students to review terms and how the words interchange with the math. Knowing the terms will help them understand the math problems, In addition, how to graph an ordered pair.
-Expectations
TSW learn the terms and how they are used in algebra problems. TSW will be able to take an ordered pair and plot it on the graph. TSW understand the terms of the operations to know how to graph ordered pairs and will learn how to plot a graph. The students will work in cooperative groups and define terms, relations and functions of the graph.
-Rationale
This lesson is taught so that students understand the graphs and the beginning of linear equations. Teaches students strategies and gives them practice with all the test item formats they will encounter on the FCAT. Error prevention: Students may forget to label their graphs. Suggest that the students begin a graph by labeling both axes. Remind them that time is often represented along the x-axis.
-Guiding Questions
Guided Practice: Lead and Support*
TSW ask related questions and check for understanding. Students will be able to ask their cooperative partners and check for understanding.
TTW explain the graph on page 400 about the can food drive. There are e6 homeroom classes that are participating in the can food drive, in those classes there are a different about of students in each class. The there are different amounts of cans that were brought in from each class. How does this relation, a set of ordered pairs. Discuss range, domain, and function.
ESOL Strategy: Explain the process, predict, Think, share and compare.
Review directions with students in small group or individually before using the handout.
Review terms and definitions.
Review reasoning and concepts with students
Provide immediate feedback about performance.
Check for understanding.
Size: TSW follow along as other students or teacher. Give oral answers as questions are asked.
Input: TTW On over head projector discuss the questions with the class. Having students write down important facts, things that you wrote on the overhead can be given to the student to take home for reinforcement of concepts.
ESOL Strategy: Give more details, simple details and answers
Output: TTW respond to questions at a lower level and the student will be able to answer fewer questions than the rest of the class. TTW be able to pick out the vocabulary words and read them out loud to the student. TSW be able to answer orally questions from the worksheet that was sent home as an assessment of progress
-Closure
Independent Practice/Cooperative Practice*
Provide web access to programs for FCAT review and math concepts practice. Chapter 8 on www.phschool.com for guided practice.
TSW have fewer questions to answer, will use vocabulary words as an alterative quiz, and have a reading buddy to help with the questions and the vocabulary words. TTW assess with oral questions and give the quiz while the other students are taking their quiz. TSW be able to have extra time if needed on quizzes and test.
Difficulty: TSW answer questions given on a work sheet.. Such as: Vocabulary words What o you think you need to do next, what is the next step?
Assessment*:
Teachers learn about student learning through multiple ways: observations, asking questions, product completion, quizzes, verbal discussions, etc. to determine mastery of lesson objectives.
TTW have students who are ready to proceed to address the rest of the problems on pages 402- 404
TTW help student with answers, leading questions like what did you like about the problems? A peer Buddy (Reading Buddy) will help student with words that they do not know and will help student sound out words that are not mastered.
Time: Reread text and work sheet if necessary, so that student can listen for the answers. TSW be allowed to answer fewer questions so that they can finish the test in the same time frame as the rest of the class.
Degree of Participation: TSW answer the questions that are given. This will be fewer than the rest of the class so that the student can finish in the same time frame. If the student needs a break, the student will be able to get up and sharpen their pencil or get a drink.
Alternate Goals:
TSW answer the same questions. They will be able to give simple answers. The student will have a reading buddy to help with the correct answers before the quiz. The quiz will be on vocabulary words and simple answer questions. There will be one higher level thinking question so that the student can get used to those kinds of questions for the standardized test.
*From Co-teaching rubric: The lesson plan reflects opportunities to work collaboratively with other professionals (e.g., co-teacher) in the continuous improvement of the educational experiences of students.
Extensions:
TSW have fewer questions to answer, will use vocabulary words as an alterative quiz, and have a reading buddy to help with the questions and the vocabulary words. TTW assess with oral questions and give the quiz while the other students are taking their quiz. TSW be able to have extra time if needed on quizzes and test.
Accommodations/Modifications:
The accommodations are in the plan size, input, output etc…
Access Points:
Independent: MA.912A.2 In.c. Identify the mathematical relationship (function) and the type of information represented in a function table or simple graph.
Supported: MA.912.A.Su.c Identify number patters and relationships using physical and visual models representing real-world situations.
Participatory: MA.912.A.2 Pa.b Compare sets to 10 of objects, pictures, or symbols using one-to-one correspondence and identify which has more or less.
Four labeled ESOL Strategies
ESOL Strategy: Give more details, simple details and answers.
ESOL Strategy: analyze, complete, define, defend and debate.
ESOL Strategy: Explain the process, predict, Think, share and compare.
ESOL Strategy: Identify main ideas and vocabulary
References
Prentice Hall Mathematics Pre- Algebra Book. Students will access this website from the book to have extra practice in the class and at home.
www.phschool.com
Florida standards for Florida:
http://www.floridastandards.org/Standards/FLStandardSearch.aspx
Vaughn, S.,Bos, C., Strategies for Teaching Students with Learning and Behavior Problems. 7th edition.2009.
Pearson. Upper Saddle River, New Jersey.
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